Estimation of hydrologic properties of heterogeneous geologic media with an inverse method based on iterated function systems

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The hydrologic properties of heterogeneous geologic media are estimated by simultaneously inverting multiple observations from well-test data. A set of pressure transients observed during one or more interference tests is compared to the corresponding values obtained by numerically simulating the tests using a mathematical model. The parameters of the mathematical model are varied and the simulation repeated until a satisfactory match to the observed pressure transients is obtained, at which point the model parameters are accepted as providing a possible representation of the hydrologic property distribution. Restricting the search to parameters that represent fractal hydrologic property distributions can improve the ...
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Description

The hydrologic properties of heterogeneous geologic media are estimated by simultaneously inverting multiple observations from well-test data. A set of pressure transients observed during one or more interference tests is compared to the corresponding values obtained by numerically simulating the tests using a mathematical model. The parameters of the mathematical model are varied and the simulation repeated until a satisfactory match to the observed pressure transients is obtained, at which point the model parameters are accepted as providing a possible representation of the hydrologic property distribution. Restricting the search to parameters that represent fractal hydrologic property distributions can improve the inversion process. Far fewer parameters are needed to describe heterogeneity with a fractal geometry, improving the efficiency and robustness of the inversion. Additionally, each parameter set produces a hydrologic property distribution with a hierarchical structure, which mimics the multiple scales of heterogeneity often seen in natural geological media. Application of the IFS inverse method to synthetic interference-test data shows that the method reproduces the synthetic heterogeneity successfully for idealized heterogeneities, for geologically-realistic heterogeneities, and when the pressure data includes noise.

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